{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2023 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# alphametic"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/alphametic.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/alphametic.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "  Generic alphametic solver in Google CP Solver.\n",
    "\n",
    "  This is a generic alphametic solver.\n",
    "\n",
    "  Usage:\n",
    "     python alphametic.py\n",
    "                         ->  solves SEND+MORE=MONEY in base 10\n",
    "\n",
    "     python alphametic.py  'SEND+MOST=MONEY' 11\n",
    "                         -> solver SEND+MOST=MONEY in base 11\n",
    "\n",
    "     python alphametic.py TEST <base>\n",
    "                         -> solve some test problems in base <base>\n",
    "                            (defined in test_problems())\n",
    "\n",
    "  Assumptions:\n",
    "  - we only solves problems of the form\n",
    "           NUMBER<1>+NUMBER<2>...+NUMBER<N-1> = NUMBER<N>\n",
    "    i.e. the last number is the sum\n",
    "  - the only nonletter characters are: +, =, \\d (which are splitted upon)\n",
    "\n",
    "\n",
    "  Compare with the following model:\n",
    "  * Zinc: http://www.hakank.org/minizinc/alphametic.zinc\n",
    "\n",
    "  This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
    "  Also see my other Google CP Solver models:\n",
    "  http://www.hakank.org/google_or_tools/\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import re\n",
    "\n",
    "from ortools.constraint_solver import pywrapcp\n",
    "\n",
    "\n",
    "def main(problem_str=\"SEND+MORE=MONEY\", base=10):\n",
    "\n",
    "  # Create the solver.\n",
    "  solver = pywrapcp.Solver(\"Send most money\")\n",
    "\n",
    "  # data\n",
    "  print(\"\\nproblem:\", problem_str)\n",
    "\n",
    "  # convert to array.\n",
    "  problem = re.split(\"[\\s+=]\", problem_str)\n",
    "\n",
    "  p_len = len(problem)\n",
    "  print(\"base:\", base)\n",
    "\n",
    "  # create the lookup table: list of (digit : ix)\n",
    "  a = sorted(set(\"\".join(problem)))\n",
    "  n = len(a)\n",
    "  lookup = dict(list(zip(a, list(range(n)))))\n",
    "\n",
    "  # length of each number\n",
    "  lens = list(map(len, problem))\n",
    "\n",
    "  #\n",
    "  # declare variables\n",
    "  #\n",
    "\n",
    "  # the digits\n",
    "  x = [solver.IntVar(0, base - 1, \"x[%i]\" % i) for i in range(n)]\n",
    "  # the sums of each number (e.g. the three numbers SEND, MORE, MONEY)\n",
    "  sums = [solver.IntVar(1, 10**(lens[i]) - 1) for i in range(p_len)]\n",
    "\n",
    "  #\n",
    "  # constraints\n",
    "  #\n",
    "  solver.Add(solver.AllDifferent(x))\n",
    "\n",
    "  ix = 0\n",
    "  for prob in problem:\n",
    "    this_len = len(prob)\n",
    "\n",
    "    # sum all the digits with proper exponents to a number\n",
    "    solver.Add(\n",
    "        sums[ix] == solver.Sum([(base**i) * x[lookup[prob[this_len - i - 1]]]\n",
    "                                for i in range(this_len)[::-1]]))\n",
    "    # leading digits must be > 0\n",
    "    solver.Add(x[lookup[prob[0]]] > 0)\n",
    "    ix += 1\n",
    "\n",
    "  # the last number is the sum of the previous numbers\n",
    "  solver.Add(solver.Sum([sums[i] for i in range(p_len - 1)]) == sums[-1])\n",
    "\n",
    "  #\n",
    "  # solution and search\n",
    "  #\n",
    "  solution = solver.Assignment()\n",
    "  solution.Add(x)\n",
    "  solution.Add(sums)\n",
    "\n",
    "  db = solver.Phase(x, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)\n",
    "\n",
    "  solver.NewSearch(db)\n",
    "\n",
    "  num_solutions = 0\n",
    "  while solver.NextSolution():\n",
    "    num_solutions += 1\n",
    "    print(\"\\nsolution #%i\" % num_solutions)\n",
    "    for i in range(n):\n",
    "      print(a[i], \"=\", x[i].Value())\n",
    "    print()\n",
    "    for prob in problem:\n",
    "      for p in prob:\n",
    "        print(p, end=\" \")\n",
    "      print()\n",
    "    print()\n",
    "    for prob in problem:\n",
    "      for p in prob:\n",
    "        print(x[lookup[p]].Value(), end=\" \")\n",
    "      print()\n",
    "\n",
    "    print(\"sums:\", [sums[i].Value() for i in range(p_len)])\n",
    "    print()\n",
    "\n",
    "  print(\"\\nnum_solutions:\", num_solutions)\n",
    "  print(\"failures:\", solver.Failures())\n",
    "  print(\"branches:\", solver.Branches())\n",
    "  print(\"WallTime:\", solver.WallTime())\n",
    "\n",
    "\n",
    "def test_problems(base=10):\n",
    "  problems = [\n",
    "      \"SEND+MORE=MONEY\", \"SEND+MOST=MONEY\", \"VINGT+CINQ+CINQ=TRENTE\",\n",
    "      \"EIN+EIN+EIN+EIN=VIER\", \"DONALD+GERALD=ROBERT\",\n",
    "      \"SATURN+URANUS+NEPTUNE+PLUTO+PLANETS\", \"WRONG+WRONG=RIGHT\"\n",
    "  ]\n",
    "\n",
    "  for p in problems:\n",
    "    main(p, base)\n",
    "\n",
    "\n",
    "problem = \"SEND+MORE=MONEY\"\n",
    "base = 10\n",
    "if len(sys.argv) > 1:\n",
    "  problem = sys.argv[1]\n",
    "if len(sys.argv) > 2:\n",
    "  base = int(sys.argv[2])\n",
    "\n",
    "if problem == \"TEST\" or problem == \"test\":\n",
    "  test_problems(base)\n",
    "else:\n",
    "  main(problem, base)\n",
    "\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 5
}
